Yes we can use Vehicles.bin and predmety.def on Mafia ver1.3.
Problem in carcyclopedia.def and carindex.def.
In different versions they differ by 4 bytes in each car. You can compare it (link) in Hex Workshop (Tools\Compare\Compare files\Resynchronizing Compare, Resync Window = 5, Match Bytes = 5).

Haha whow. I viewed this page from the bottom up and wanted to comment that this looked similar to some mods that Axel Rokus once made. Then I saw it was you who made it. Fantastic work!
I love mods like this! _________________

I have a big problem: if I want to get out of the vehicle, my character will disappear, and this time I can not do anything, just reload the freeride extreme. Please fix this problem

Unfortunately there is nothing i can fix because i never had problems like that.
This Mod is for Mafia version 1.0
If you have a version higher than 1.0 you can delete carcyclopedia.def and carindex.def.
Anyway i canīt imagine that this is causing your problems.
Also donīt mix up different mods. If you have installed more than one mod at once
they may interfere with each other, may causing that kind of problems.

I have no idea what happened.
Maybe its the stolen copy of the game causing that problem.
If you have tried the change model option (see Pic) with no success i have no idea what you can do else.
Regards_________________